Preheat the oven to 325°F. In a large mixing bowl, sift together the flour, sugar, baking powder, and salt. In the bowl of a stand mixer, beat the egg yolks until thick and fluffy, about 3 minutes. Beat in the orange juice, oil, ¼ cup water, the vanilla, orange zest, and lemon zest. Make a well in the flour mixture and pour in the orange mixture, beating until smooth, about 5 minutes. In a clean bowl, beat the egg whites on high speed until they begin to foam. Add the cream of tartar and beat until the whites form stiff peaks. Gently fold the egg whites into the batter.
Pour the batter into an ungreased 13 by 18-inch rimmed baking sheet, smooth the top, and bake for 25 to 30 minutes, or until the cake springs back when touched. Let cool completely in the pan.
Find a domed metal bowl with an 8-inch diameter or use a spare bowl from your stand mixer. Pack the softened ice cream into the bowl (if you’re using the mixer bowl it won’t be completely full), making sure to press it in firmly to avoid air pockets. Place the bowl in the freezer to refreeze the ice cream.
To assemble the baked Alaska, place a round cake pan or plate about 1 inch larger in diameter than the ice cream bowl on top of the sheet cake and carefully cut around it with a knife (save the scraps for snacks or lunch boxes). Place the cake round on a plate. Dampen a clean kitchen towel and heat it in the microwave for 30 seconds. Remove the bowl of ice cream from the freezer and wrap the towel around the bowl for a minute to loosen the ice cream. Quickly invert the ice cream dome onto the cake round. The ice cream dome should be centered on the cake. Place the baked Alaska in the freezer for 10 minutes to firm the ice cream again.
Preheat the oven to 500°F while you make the Swiss meringue. (If you have a kitchen torch you can skip the preheating.)
Transfer the Swiss meringue to a pastry bag fitted with a 1-inch plain round tip. Quickly dot the entire cake with meringue spikes, covering the ice cream completely. (If you don’t have a pastry bag, simply use a spatula to cover the entire cake. Although it will not have the same dramatic effect, it will taste just as good.) Slide the cake into the oven to brown the meringue, about 6 to 8 minutes, or brown the meringue with a kitchen torch. Serve immediately.